Cutting Carrot

2000ms

262144K

Description:

Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area.

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

$\text{[math]}$ Illustration to the first example.

Input:

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 10⁵).

Output:

The output should contain n - 1 real numbers x₁, x₂, ..., x_n - 1. The number x_i denotes that the i-th cut must be made x_i units away from the apex of the carrot. In addition, 0 < x₁ < x₂ < ... < x_n - 1 < h must hold.

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10^- 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if $\text{[math]}$ .

Sample Input:

3 2

Sample Output:

1.154700538379 1.632993161855

Sample Input:

2 100000

Sample Output:

70710.678118654752

Note:

Definition of isosceles triangle: https://en.wikipedia.org/wiki/Isosceles_triangle.

Informação

Provedor Codeforces

Código CF794B